A crystallographic bar-joint framework, C in R, is shown to be almost periodically infinitesimally rigid if and only if it is strictly periodically infinitesimally rigid and the rigid unit mode (RUM) spectrum, Ω(C), is a singleton. Moreover, the almost periodic infinitesimal flexes of C are characterised in terms of a matrix-valued function, ΦC(z), on the d-torus, T, determined by a full rank t...

We consider operators of convolution generated by L func tions in L and various spaces of almost periodic functions It turns out to be that if such an operator is invertible in one of these spaces then it is in vertible in all the spaces we consider Further we prove that any convolution has identical norms in many natural couples of functional spaces

This paper answers negatively the question of whether the sets of idempotents in the weakly almost periodic compactifications of (N, +) and (Z, +) are closed.

A factorization theory is proposed for Wiener-Hopf plus Hankel operators with almost periodic Fourier symbols. We introduce a factorization concept for the almost periodic Fourier symbols such that the properties of the factors will allow corresponding operator factorizations. Conditions for left, right, or both-sided invertibility of the Wiener-Hopf plus Hankel operators are therefore obtained...

A density on a locally compact Abelian group G is a bounded system of compatible measures on the compact quotients of G. The notion of density arises naturally both in connection with the theory of uniform distribution and with the theory of almost periodic functions. Our main result effectively answers the question "when are all densities on G induced by measures on some compactification of G?...

In this note we communicate some important remarks about the concepts of almost periodic time scales and almost periodic functions on time scales that are proposed by Wang and Agarwal in their recent papers ( see [7]-[10]).

In this paper, we study the existence and uniqueness solution and investigate the conditions that make it almost-periodic solution for BAM neural networks with retarded delays. The existence of solution established by using Schauder fixed point theorem. The uniqueness established by using Banach fixed point theorem. Moreover we study the parametric stability of such a solution. Also we illustra...

This paper deals with fuzzy cellular neural networks (FCNNs) with leakage delays and proportional delays. Applying the differential inequality strategy, fixed point theorem and almost periodic function principle, some sufficient criteria which ensure the existence and global attractivity of a unique almost periodic solution for fuzzy cellular neuralnetworks with leakage delays and p...